Question

3х-7<х+1 2) 2+х>8-х 3) 1-х≤2х-5 4)2х+1>х+6 5) 4х+2>3х+1 6)6х+1<2х+9

Answer 1

все на листочке все правильно не волнуйся

Answer 2

Let's solve the given inequalities one by one:

1. 3x - 7 < x + 1:

To solve this inequality, we'll isolate the variable x.

Subtract x from both sides: 3x - x - 7 < x - x + 1

Simplifying the left side: 2x - 7 < 1

Add 7 to both sides: 2x - 7 + 7 < 1 + 7

Simplifying the left side: 2x < 8

Divide both sides by 2 (since the coefficient of x is 2): 2x/2 < 8/2

Simplifying the equation: x < 4

Therefore, the solution for the inequality 3x - 7 < x + 1 is x < 4.

2. 2 + x > 8 - x:

To solve this inequality, we'll isolate the variable x.

Add x to both sides: 2 + x + x > 8 - x + x

Simplifying the equation: 2x + 2 > 8

Subtract 2 from both sides: 2x + 2 - 2 > 8 - 2

Simplifying the equation: 2x > 6

Divide both sides by 2: 2x/2 > 6/2

Simplifying the equation: x > 3

Therefore, the solution for the inequality 2 + x > 8 - x is x > 3.

3. 1 - x ≤ 2x - 5:

To solve this inequality, we'll isolate the variable x.

Add x to both sides: 1 - x + x ≤ 2x - 5 + x

Simplifying the equation: 1 ≤ 3x - 5

Add 5 to both sides: 1 + 5 ≤ 3x - 5 + 5

Simplifying the equation: 6 ≤ 3x

Divide both sides by 3: 6/3 ≤ 3x/3

Simplifying the equation: 2 ≤ x

Therefore, the solution for the inequality 1 - x ≤ 2x - 5 is x ≥ 2.

4. 2x + 1 > x + 6:

To solve this inequality, we'll isolate the variable x.

Subtract x from both sides: 2x + 1 - x > x + 6 - x

Simplifying the equation: x + 1 > 6

Subtract 1 from both sides: x + 1 - 1 > 6 - 1

Simplifying the equation: x > 5

Therefore, the solution for the inequality 2x + 1 > x + 6 is x > 5.

5. 4x + 2 > 3x + 1:

To solve this inequality, we'll isolate the variable x.

Subtract 3x from both sides: 4x + 2 - 3x > 3x + 1 - 3x

Simplifying the equation: x + 2 > 1

Subtract 2 from both sides: x + 2 - 2 > 1 - 2

Simplifying the equation: x > -1

Therefore, the solution for the inequality 4x + 2 > 3x + 1 is x > -1.

6. 6x + 1 < 2x + 9:

To solve this inequality, we'll isolate the variable x.

Subtract 2x from both sides: 6x + 1 - 2x < 2x + 9